Problem: Simplify the following expression: $ z = \dfrac{-7}{8} - \dfrac{-10}{-5n - 2} $
Answer: In order to subtract expressions, they must have a common denominator. Multiply the first expression by $\dfrac{-5n - 2}{-5n - 2}$ $ \dfrac{-7}{8} \times \dfrac{-5n - 2}{-5n - 2} = \dfrac{35n + 14}{-40n - 16} $ Multiply the second expression by $\dfrac{8}{8}$ $ \dfrac{-10}{-5n - 2} \times \dfrac{8}{8} = \dfrac{-80}{-40n - 16} $ Therefore $ z = \dfrac{35n + 14}{-40n - 16} - \dfrac{-80}{-40n - 16} $ Now the expressions have the same denominator we can simply subtract the numerators: $z = \dfrac{35n + 14 + 80 }{-40n - 16} $ Distribute the negative sign: $z = \dfrac{35n + 14 + 80}{-40n - 16}$ $z = \dfrac{35n + 94}{-40n - 16}$ Simplify the expression by dividing the numerator and denominator by -1: $z = \dfrac{-35n - 94}{40n + 16}$